Phương pháp giải:

$\mathop {\lim }\limits_{x \to \infty } \left[ {f\left( x \right) + g\left( x \right)} \right] = \mathop {\lim }\limits_{x \to \infty } f\left( x \right) + \mathop {\lim }\limits_{x \to \infty } g\left( x \right)$.

Lời giải chi tiết:

$\mathop {\lim }\limits_{} \left( {{u_n} + \dfrac{{{2^n}}}{{{2^n} + 3}}} \right) = \lim {u_n} + \lim \dfrac{{{2^n}}}{{{2^n} + 3}} = \lim {u_n} + \lim \dfrac{1}{{1 + \dfrac{3}{{{2^n}}}}} = 2 + 1 = 3$.

Chọn C.